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Single-crystal neutron diffraction, inelastic neutron scattering, bulk magnetization measurements are used to investigate the magnetic properties of honeycomb lattice Tb₂Ir₃Ga₉. While the R ln 2 magnetic contribution to the low-temperature entropy indicates a J_eff = 1/2 moment for the lowest-energy crystal-field doublet, the Tb3+ ions form a canted antiferromagnetic structure below 12.5 K. Due to the Dzyaloshinskii-Moriya interactions, the Tb moments in the ab plane are slightly canted towards b with a moment of 1.22 μB per formula unit. A minimal xxz spin Hamiltonian is used to simultaneously fit the spin-wave frequencies along the high-symmetry directions and the field dependence of the magnetization along the three crystallographic axes. Second nearest neighbors interactions for both in-plane and out-of-plane couplings are needed to account for the observed static and dynamic properties. The z component between Tb moments is larger than the x and y components. The nearest-neighbor exchange coupling between moments parallel and perpendicular to the 4f orbitals is negligible. Despite the J_eff = 1/2 moments, the spin Hamiltonian is denominated by a large in-plane anisotropy K_z.The observed diffuse scattering features indicate considerable 3D magnetic correlations along c.